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Homework Help: Components of E field

  1. Sep 26, 2016 #1
    1. The problem statement, all variables and given/known data
    Grounded conducting sphere in uniform electric field has potential
    V(r,θ) = -Vo(1 - (R/r)3)*cosθ

    Find Er and Eθ.
    2. Relevant equations

    3. The attempt at a solution
    In the text book I found
    Er = -∂V/∂r

    Eθ = -1/r ∂V/∂θ

    Those are in the chapter we're working with but those two equations are in the section talking about the electric field of dipoles. Do those equations apply for the problem I'm working on?
  2. jcsd
  3. Sep 27, 2016 #2

    Simon Bridge

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    By definition: ##\vec E = -\vec\nabla V## ... you will need ##\nabla## in spherical-polar coordinates.

    Check how the equations in your book were derived - make sure you understand the reasoning involved. Then you can make a determination about how appropriate they are for your situation.
  4. Sep 27, 2016 #3
    the front of the book has a legend for the gradient in spherical coordinates so i used that. the question was just worded weird.

    also, the question asks for "surface charge distribution of the sphere".
    is that just the surface charge density?

    σ = q/A?
  5. Sep 27, 2016 #4
    or ρ = ∈o∇E
  6. Sep 27, 2016 #5

    Simon Bridge

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    Then you have the answer to your first question - well done.

    This is another odd wording I think. You seem quite good at figuring this stuff out...
    How would you normally express a charge distribution?
  7. Sep 28, 2016 #6
    The word "distribution" is what's throwing me off but if this were an exam I'd say it's asking for area charge density. That's how the charge is distributed over the surface per unit area.
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